Competency Focused
Practice Questions
Mathematics | Grade 10
Co-created by
Centre for Excellence in Assessment
CBSE
and
Educational Initiatives
, Preface
Assessments are an important tool that help gauge learning. They provide valuable feedback about
the effec veness of instruc onal methods; about what students have actually understood and also
provide ac onable insights. The Na onal Educa on Policy 2020 has outlined the importance of
competency-based assessments in classrooms as a means to reform curriculum and pedagogical
methodologies. The policy emphasizes on the development of higher order skills such as analysis,
cri cal thinking and problem solving through classroom instruc ons and aligned assessments.
Central Board of Secondary Educa on (CBSE) has been working closely with Educa onal Ini a ves
(Ei) in the area of assessment and capacity of the board. Through resources like the Essen al
Concepts document and A-Ques on-A-Day (AQAD), high quality assessment ques ons and concepts
cri cal to learning have been shared with schools and teachers.
Con nuing with the vision to ensure that every student is learning with understanding, Ques on
Booklets have been created for five subjects of Grade 10. These booklets contain competency-based
items, designed specifically to test conceptual understanding and applica on of concepts.
Process of crea ng competency-based items
All items in these booklets are aligned to the NCERT curriculum and have been created keeping in
mind the learning outcomes that are important for students to understand and master. Items are a
mix of subjec ve ques ons and Mul ple-Choice Ques ons (MCQs). In case of MCQs, the op ons
(correct answer and distractors) are specifically created to test for understanding and capturing
specific errors/misconcep ons that students may harbour. Each incorrect op on can thereby inform
teachers on specific gaps that may exist in student learning. In case of subjec ve ques ons, each
ques on also has a a detailed scoring rubric to guide evalua on of students’ responses.
Each item has been reviewed twice by the experts, to check for appropriateness of the item, validity
of the item, conceptual correctness, language accuracy and other nuances. The process is designed
to increase the quality of each ques on.
How can these item booklets be used?
The purpose of these item booklets is to provide samples of high-quality competency-based items to
teachers. The items can be used to–
• get an understanding of what good competency-based ques ons could look like
• give exposure to students to competency-based items
• assist in classroom teaching and learning
• to get inspira on to create more such competency-based items
Students can also use this document to understand different kinds of ques ons and prac ce specific
concepts and competencies.
Please write back to us if there is any feedback.
Team CBSE
1
, Table of Contents
1. Chapter - 1 Real Numbers
Ques ons ............................................................4
Answers key ............................................................7
2. Chapter - 2 Polynomials
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3. Chapter - 3 Pair of Linear Equa ons in Two Variables
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4. Chapter - 4 Quadra c Equa ons
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5. Chapter - 5 Arithme c Progressions
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6. Chapter - 6 Triangles
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7. Chapter - 7 Coordinate Geometry
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8. Chapter - 8 Introduc on to Trigonometry
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
9. Chapter - 9 Some Applica ons of Trigonometry
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
10. Chapter - 10 Circles
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
11. Chapter - 11 Construc ons
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
12. Chapter - 12 Areas Related to Circle
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
13. Chapter - 13 Surface Areas and Volumes
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
14. Chapter - 14 Sta s cs
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
15. Chapter - 15 Probability
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
16. Chapter - 16 Mul ple Concepts
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
2
, Chapter - 1
Real Numbers
3
Practice Questions
Mathematics | Grade 10
Co-created by
Centre for Excellence in Assessment
CBSE
and
Educational Initiatives
, Preface
Assessments are an important tool that help gauge learning. They provide valuable feedback about
the effec veness of instruc onal methods; about what students have actually understood and also
provide ac onable insights. The Na onal Educa on Policy 2020 has outlined the importance of
competency-based assessments in classrooms as a means to reform curriculum and pedagogical
methodologies. The policy emphasizes on the development of higher order skills such as analysis,
cri cal thinking and problem solving through classroom instruc ons and aligned assessments.
Central Board of Secondary Educa on (CBSE) has been working closely with Educa onal Ini a ves
(Ei) in the area of assessment and capacity of the board. Through resources like the Essen al
Concepts document and A-Ques on-A-Day (AQAD), high quality assessment ques ons and concepts
cri cal to learning have been shared with schools and teachers.
Con nuing with the vision to ensure that every student is learning with understanding, Ques on
Booklets have been created for five subjects of Grade 10. These booklets contain competency-based
items, designed specifically to test conceptual understanding and applica on of concepts.
Process of crea ng competency-based items
All items in these booklets are aligned to the NCERT curriculum and have been created keeping in
mind the learning outcomes that are important for students to understand and master. Items are a
mix of subjec ve ques ons and Mul ple-Choice Ques ons (MCQs). In case of MCQs, the op ons
(correct answer and distractors) are specifically created to test for understanding and capturing
specific errors/misconcep ons that students may harbour. Each incorrect op on can thereby inform
teachers on specific gaps that may exist in student learning. In case of subjec ve ques ons, each
ques on also has a a detailed scoring rubric to guide evalua on of students’ responses.
Each item has been reviewed twice by the experts, to check for appropriateness of the item, validity
of the item, conceptual correctness, language accuracy and other nuances. The process is designed
to increase the quality of each ques on.
How can these item booklets be used?
The purpose of these item booklets is to provide samples of high-quality competency-based items to
teachers. The items can be used to–
• get an understanding of what good competency-based ques ons could look like
• give exposure to students to competency-based items
• assist in classroom teaching and learning
• to get inspira on to create more such competency-based items
Students can also use this document to understand different kinds of ques ons and prac ce specific
concepts and competencies.
Please write back to us if there is any feedback.
Team CBSE
1
, Table of Contents
1. Chapter - 1 Real Numbers
Ques ons ............................................................4
Answers key ............................................................7
2. Chapter - 2 Polynomials
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3. Chapter - 3 Pair of Linear Equa ons in Two Variables
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4. Chapter - 4 Quadra c Equa ons
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5. Chapter - 5 Arithme c Progressions
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6. Chapter - 6 Triangles
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7. Chapter - 7 Coordinate Geometry
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8. Chapter - 8 Introduc on to Trigonometry
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
9. Chapter - 9 Some Applica ons of Trigonometry
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
10. Chapter - 10 Circles
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
11. Chapter - 11 Construc ons
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
12. Chapter - 12 Areas Related to Circle
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
13. Chapter - 13 Surface Areas and Volumes
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
14. Chapter - 14 Sta s cs
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
15. Chapter - 15 Probability
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
16. Chapter - 16 Mul ple Concepts
Ques ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Answers key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
2
, Chapter - 1
Real Numbers
3
